1. Field of the Invention
This invention relates to a quadrupole mass spectrometer or quadrupole mass filter.
2. Description of the Prior Art
The quadrupole mass spectrometer generally, as shown in FIG. 1, consists of an ion source 1, a quadrupole electrode 2 and a detector 3 including secondary electron multiplier. The quadrupole electrode 2 is constituted by four parallel rod electrodes 2a, 2b, 2c and 2d ideally of hyperbolic cross section (often merely cylindrical). Between opposite pairs of the quadrupole rod electrodes 2a, 2b, 2c and 2d overlapping voltage, .+-.(U+Vcos .omega.t) are applied as shown in FIG. 2. In the added (overlapping) voltage, a continuous voltage U or a direct current voltage U and high (radio) frequency voltage (V cos .omega.t) are added to each other. An electric field is generated in the electrodes 2a, 2b, 2c and 2d by the applied voltage. When the ions produced in the ion source 1 are introduced along the central axis (hereafter called "Z axis direction") into the quadrupole electrode 2, the ions receive forces in x axis direction and y axis direction along the z axis direction. And under certain conditions of voltages (U, V), the distance 2r.sub.0 between the opposite electrodes of the quadrupole electrode 2 and high frequency f(.omega./2.pi.), only ions having specific m/e (the ratio of mass to charge) vibrate with the limited amplitude in the x axis and y axis direction and can pass through the quadrupole electrode 2. The amplitudes of other ions having the other value m/e increase further. Accordingly, they are caught by the quadrupole rod electrode 2a, 2b, 2c or 2d or they pass through the spaces between the rod electrodes 2a, 2b, 2c and 2d. Thus, the other ions having the other value m/e can not reach the detector 3.
The ions passing though the quadrupole electrode 2 are detected by an ion collector or the secondary electron multiplier. A signal in level proportional to the ion currents is recorded by an oscilloscope, an electromagnetic oscillograph and a pen recorder. Thus, mass spectrum can be obtained.
Next, there will be described the theory of the quadrupole mass spectrometer in more detail. The potential .phi. fulfilling the following equation (1-1) is formed in the quadrupole rod electrodes 2a, 2b, 2c and 2d: The potential .phi. follows the Poisson's law. Accordingly, it fulfills the equation (1-2): EQU .phi.=.phi..sub.0 (.lambda.x.sup.2 +.sigma.y.sup.2 +.gamma.z.sup.2) (1-1)
(where .lambda., .sigma. and .gamma. are constant.) ##EQU1##
From the equations (1-1), 1-2), the following equation (1-3) can be easily obtained: EQU .lambda.+.sigma.+.gamma.=0 (1-3)
In the quadrupole mass spectrometer, these constants .lambda., .sigma. and .gamma. are selected as shown in the following equation (1-4). ##EQU2##
Accordingly, the equation (1-1) can be expressed as shown in the following equation (1-5): ##EQU3##
The shape of the cross section of the rod electrodes forming the above potential .phi. is of rectangular hyperbola. It is characterized in a quadrupole mass spectrometer. As shown in FIG. 2, the added or overlapping voltage .+-.(U+V cos.omega.t) is applied to the rod electrodes 2a, 2b, 2c and 2d. Thus, the potential represented by the following equation (1-6) is formed in the quadrupole electrode 2. ##EQU4##
The potential gradient or the electric field in the quadrupole electrode 2 can be represented by the following equation (1-7): ##EQU5##
The equation of motion of the ion passing through the above described electric field is expressed by the following equation (1-8). ##EQU6##
Next, there will be considered motions of the ion. The motions in x axis direction and y axis direction can be independently handled. The ions receive periodical forces in x axis direction and y axis direction. Thus, the ions vibrate in the x axis direction and y axis direction. They receive no force in the z axis direction. Accordingly, they move at the same rate as initial velocity in the Z axis direction. When the equation (1-8) is substituted for the equation (1-9), the differential equation (1-10) which is known as the Mathieu's equation, can be obtained: ##EQU7##
The motion of the ion in the electric field formed by the quadrupole rod electrodes can be obtained by the solution of the above equation. The solution consists of a stable solution and a unstable solution.
In the stable solution, the ions can take the stable orbit within a predetermined amplitude for an indefinite time. In the unstable solution,the amplitude of the motion of the ions indefinitely increases with time. The relationship between an and q for giving the stable solutions can be shown in the (a, q) plane. It is shown in FIG. 3. The regions for the stable solution of the x axis direction and y axis direction in the electric field of the quadrupole electrode 2 are symmetrical with respect to the original point as shown in FIG. 3. The hatched portions correspond to the region for the stable solution and the white (non-hatched) portion correspond to the region for the unstable solution. In order that the ion can pass through the electric field of the quadrupole electrode 2, the amplitude of the motion of the ions in the x axis direction and y axis direction should be limited within a certain value. This fact means that the stable region for x axis direction and the stable region for y axis direction should overlap with each other. In a practical quadrupole mass spectrometer, the stable region nearest to the original point is utilized from a practical view point. The stable region is enlargedly shown in FIG. 7. It is called "stability diagram".
One point on the (a,q) plane corresponds to the ion having the predetermined mass when the values of r.sub.0, .omega. and the voltages U and V are determined. The relationship a/2q=U/V is obtained from the equation (1-9). Thus, the line passes through the original point on the (a,q) plane and it has the gradient which is determined by a ratio of U to V. It has no relationship with a mass number. When the ratio U/V is determined, the ions having the different masses are aligned on the line. Such a line is called "mass scan line". Only the ions having the mass on the line portion in the stable region, as through the electric field of the quadrupole rod electrodes 2a, 2b, 2c, and 2d. The ions in the y stable region and x unstable region out of the xy stable region on the line have a larger mass than the ions in the xy stable region. Such ions in x axis direction are unstable in motion and so they are captured by the one of the quadrupole rod electrodes 2c, 2d on x axis. The other hand, the ions in the x stable region and the y unstable region out of the xy stable region have smaller mass than the ions in the xy stable region. Such ions are unstable in motion in axis direction and it is captured by the one of the quadruple rod electrodes 2a, 2b in the y axis direction.
In the above-mentioned manner, the ion mass can be analyzed. However, when the above described quadrupole mass spectrometer is used, the ratio of U/V is varied in order to adjust the resolution-power. The more the ratio of U/V is enlarged, the gradient of mass scan line in FIG. 7 is steeper. At last, the mass scan line passes through a Q point which is a top point of the xy stable region. However, the mass scan line passing through the point near the top point Q has a higher resolution-power.
Next, there will be described the above-mentioned fact with respect to FIG. 4. From the mass scan line with a relatively small ratio of U/V, a spectrum shown in FIG. 4A can be obtained. At both sides of the ion having the mass which correspond to the point a, the peaks of the ions b, c can be found, which have larger and smaller masses respectively than the mass corresponding to the point a. However, such spectrum can be distinguished differently from each other only by the degree of observer's skill. Some person may read this spectrum as only an ion having the mass a. In order to improve the resolution-power more, the ratio of U/V should be increased and so the U value is adjusted. Accordingly, the spectrum as shown in FIG. 4B can be obtained. When the ratio of U/V is increased further for high resolution-power, a spectrum as shown in FIG. 4C can be obtained.
However, even when a high resolution-power is set, it varies daily with a thermal drift or reliability of the circuit parts in the circuit constructions. Accordingly, whenever the same mass spectrometer is used, subtle adjustment should be made. Thus, the reproducibility is difficult to be obtained for the same mass spectrometer.